You'll meet so many people - more as a single gal than travelling with a friend. Loneliness is highly unlikely!
Take along a book or grab an international newspaper if it looks like you'll be dining or at a cafe alone, that way you look more confident (and feel more comfortable) than sitting there staring at your empty placemat, and if someone starts paying you unwanted attention, you can just excuse yourself and reapply yourself to your reading material. If you pick something obscure like "The Origin of Species", you can be sure that it will last you the entire trip, and it looks like you're doing research or something.
I also tried to carry a pen and small notebook around, so that I could doodle, make notes, plan my next adventure or write someone at home, which also can help you feel less alone.